SOLUTION: Given: cos A = 3/5, tan B = 12/5, A is in Q1 and is in Q3 Find Sin (A + B)

Algebra ->  Trigonometry-basics -> SOLUTION: Given: cos A = 3/5, tan B = 12/5, A is in Q1 and is in Q3 Find Sin (A + B)      Log On


   

Question 1181124: Given: cos A = 3/5, tan B = 12/5, A is in Q1 and is in Q3
Find Sin (A + B)
Answer by ikleyn(52852) About Me  (Show Source):
You can put this solution on YOUR website!
.

cos A = 3%2F5,  A is in Quadrant 1 

sin A = sqrt%281-cos%5E2%28A%29%29 = sqrt%281-%283%2F5%29%5E2%29 = sqrt%281-%289%2F25%29%29 = sqrt%2816%2F25%29%29 = 4%2F5, 

cos A = 3%2F5, tan A = 4%2F3


tan B = 12%2F5, quadrant III  

tan B = 12%2F5, sin B = -12%2F13, cos B = -5%2F13


sin (A + B) = sin(A)cos(B) + cos(A)sin(B) = %284%2F5%29%28-5%2F13%29 + %283%2F5%29%28-12%2F13%29 = -20%2F65 - 36%2F65 = -56%2F65.

Solved.

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To see many other similar solved problems on calculating trig functions,  look into the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
    - Evaluating trigonometric expressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Trigonometry: Solved problems".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.